Diffusion in the mean for a periodic Schrödinger equation perturbed by a fluctuating potential

Abstract

We consider the evolution of a quantum particle hopping on a cubic lattice in any dimension and subject to a potential consisting of a periodic part and a random part that fluctuates stochastically in time. If the random potential evolves according to a stationary Markov process, we obtain diffusive scaling for moments of the position displacement, with a diffusion constant that grows as the inverse square of the disorder strength at weak coupling. More generally, we show that a central limit theorem holds such that the square amplitude of the wave packet converges, after diffusive rescaling, to a solution of a heat equation.

41 pages, 1 figure

References in corpus (5)

• Quantum Dynamics of Periodic and Limit-Periodic Jacobi and Block Jacobi Matrices with Applications to Some Quantum Many Body Problems
• Diffusion of wave packets in a Markov random potential
• Ballistic Transport for the Schrödinger Operator with Limit-Periodic or Quasi-periodic Potential in Dimension Two
• Transport of a quantum particle in a time-dependent white-noise potential
• Quantum Brownian motion induced by thermal noise in the presence of disorder